Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin

Quantum Hoare logic with classical variables

Hoare logic provides a syntax-oriented method to reason about program correctness, and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness or support only quantum variables, thus limiting their capability in practical use. In this paper, we propose a quantum Hoare logic for a simple while language which involves both classical and quantum variables. Its soundness and relative completeness are proven for both partial and total correctness of quantum programs written in the language. Remarkably, with novel definitions of classical-quantum states and corresponding assertions, the logic system is quite simple and similar to the traditional Hoare logic for classical programs. Furthermore, to simplify reasoning in real applications, auxiliary proof rules are provided which support the introduction of disjunction and quantifiers in the classical part of assertions, and of super-operator application and superposition in the quantum part. Finally, a series of practical quantum algorithms, in particular the whole algorithm of Shor's factorisation, are formally verified to show the effectiveness of the logic

A Deductive Verification Framework for Circuit-building Quantum Programs

While recent progress in quantum hardware open the door for significant speedup in certain key areas, quantum algorithms are still hard to implement right, and the validation of such quantum programs is a challenge. Early attempts either suffer from the lack of automation or parametrized reasoning, or target high-level abstract algorithm description languages far from the current de facto consensus of circuit-building quantum programming languages. As a consequence, no significant quantum algorithm implementation has been currently verified in a scale-invariant manner. We propose Qbricks, the first formal verification environment for circuit-building quantum programs, featuring clear separation between code and proof, parametric specifications and proofs, high degree of proof automation and allowing to encode quantum programs in a natural way, i.e. close to textbook style. Qbricks builds on best practice of formal verification for the classical case and tailor them to the quantum case: we bring a new domain-specific circuit-building language for quantum programs, namely Qbricks-DSL, together with a new logical specification language Qbricks-Spec and a dedicated Hoare-style deductive verification rule named Hybrid Quantum Hoare Logic. Especially, we introduce and intensively build upon HOPS, a higher-order extension of the recent path-sum symbolic representation, used for both specification and automation. To illustrate the opportunity of Qbricks, we implement the first verified parametric implementations of several famous and non-trivial quantum algorithms, including the quantum part of Shor integer factoring (Order Finding - Shor-OF), quantum phase estimation (QPE) - a basic building block of many quantum algorithms, and Grover search. These breakthroughs were amply facilitated by the specification and automated deduction principles introduced within Qbricks

Qafny: Quantum Program Verification Through Type-guided Classical Separation Logic

Formal verification has been proven instrumental to ensure that quantum programs implement their specifications but often requires a significant investment of time and labor. To address this challenge, we present Qafny, an automated proof system designed for verifying quantum programs. At its core, Qafny uses a type-guided quantum proof system that translates quantum operations to classical array operations. By modeling these operations as proof rules within a classical separation logic framework, Qafny automates much of the traditionally tedious and time-consuming reasoning process. We prove the soundness and completeness of our proof system and implement a prototype compiler that transforms Qafny programs both into the Dafny programming language and into executable quantum circuits. Using Qafny, we demonstrate how to efficiently verify important quantum algorithms, including quantum-walk algorithms, Grover's search algorithm, and Shor's factoring algorithm, with significantly reduced human effort.Comment: Version

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Toward automatic verification of quantum programs

Programming is error-prone. It is even worse when programming a quantum computer or designing quantum communication protocols, because human intuition is much better adapted to the classical world than to the quantum world. How can we build automatic tools for verifying correctness of quantum programs? A logic for verification of both partial correctness and total correctness of quantum programs was developed in our TOPLAS'2011 paper. The (relative) completeness of this logic was proved. Recently, a theorem prover for verification of quantum programs was built based on this logic [arXiv: 1601.03835]. To further develop automatic tools, we are working on techniques for invariant generation and synthesis of ranking functions for quantum programs.Non UBCUnreviewedAuthor affiliation: University of Technology SydneyFacult

Toward automatic verification of quantum programs.

This paper summarises the results obtained by the author and his collaborators in a program logic approach to the verification of quantum programs, including quantum Hoare logic, invariant generation and termination analysis for quantum programs. It also introduces the notion of proof outline and several auxiliary rules for more conveniently reasoning about quantum programs. Some problems for future research are proposed at the end of the paper